Stata Economic Assignment Homework

Question 11. The data file Loanapp.dta contains information from mortgage applications made in the Boston area in 1990, and a follow up survey of the banks and other lending institutions that received these mortgage applications. These data were originally used in a famous study by researchers at the Boston Federal Reserve Bank. This dataset is a subset of that original data. The binary variable to be explained is approve, which is equal to 1 if a mortgage loan to an individual is approved. The key explanatory variable is white, a dummy variable equal to one if the applicant was white. The other applicants in the dataset are black and Hispanic.To test for discrimination in the mortgage loan market, a linear probability model can be used: approve=?0+?1 white + other factors.If there is discrimination against minorities, and the appropriate factors have been controlled for, we expect ?1 to be Term 1 .5 points Question 21. Regress approve on white. Interpret the results: the probability of getting your loan approved is Blank 1 percent (round your answer to 1 decimal point) Blank 2 (higher/lower) if you are a white person rather than an African-American person or an Hispanic person.10 points Question 31. To avoid omitted variable bias, you want to keep constant financial variables such as housing expense-to-income ratio (hrat), and loan-to-ratio (loanprc), and other applicant characteristics such as gender (male) and marital status (married). Thus, as controls add the following 14 variables: hrat, obrat, loanprc, unem, male, married, dep, sch, cosign, chist, pubrec, mortlat1, mortlat2, vr. (Note: the meaning of most of the variables can be made clear if you look at their labels in the window Variables in Stata). Relative to the single regression model, the coefficient on white on this multiple regression model goes Blank 1 (up/down). Is there evidence of discrimination against minorities? Blank 2 (Yes/No)10 points Question 41. Graph the predicted probabilities of loan approval with loanprc in the x-axis, for whites and nonwhites. You should have two separate lines, one for whites and another for non-whites, with loanprc in the horizontal axis and predicted probabilities in the vertical axis. Use intervals of 0.2 for loanprc. In order to achieve that you have first to enter a margins command, specifying the values at which you want the predicted probality to be evaluated at. Keep all the dummy variables at 1 and the rest of the variables at their means. (Hint: If you need, you may use estat sum to describe the variables in the above regression, to check which ones are dummies and which ones are not).margins, at(white=(0(1)1) loanprc=(0(0.2)2.6) …. specify the values for all the variables)Look at the stata tutorial file for more about the margins command.Then, to create the plot, you need to write the command marginsplot with the following options:marginsplot, plot(white) nociThe output should display two plots with loanprc in the x-axis and predicted probabilities in the y-axis, one plot for white people and another for nonwhite people.What is the difference between probability of loan approval for a white person versus a non-white person with a loanprc of 0.8 and all the other variables at the values specified? Your answer should be expressed in percentage points (Specify 3 decimal points, for example if the difference between the two probabilities is 15.3%, enter 0.153 in your answer)5 points Question 51. Compute predicted probabilities of loan approval for each person in the sample. How many predicted probability values are above 1? Blank 1 . How many probability values are below 0? Blank 2 .10 points Question 61. Using the same dataset, estimate a probit model of approve on white only. According to this model, what is the difference between estimated probability of loan approval for whites vs nonwhites? (use three decimal points – for example a probability difference of 15.8% would be presented as 0.158)5 points Question 71. Compare the difference in estimated probabilities of loan approval between whites and non-whites in the probit regression (question 6) and in the LPM regression (question 2) for the case of one unique regressor (the dummy variable regressor white). How does the estimated probability difference in the probit regression compare with the estimated probability difference in the LPM regression? They are exactly the same. The difference in estimated probabilities between whites and non-whites is higher in the single regression probit than in the single regression LPM. The difference in estimated probabilities between whites and non-whites is lower in the single regression probit than in the single regression LPM. None of the above.5 points Question 81. Add the same variables as in question 3 to your probit model and estimate. Is there statistical significant evidence of discrimination against minorities? Blank 1 (Yes/No), since the estimated coefficient on white is Blank 2 (positive/negative) and the relevant t-statistic is equal to Blank 3 (use 2 decimal points).15 points Question 91. Compute predicted probabilities of loan approval for the different values of the explanatory variable dep. What is the probability of approval for an applicant with 6 dependents, keeping all the other variables at their means? (use 3 decimal points – a probability of 65.4% should be entered as 0.654)5 points Question 101. Graph the predicted values of approve with loanprc in the x-axis, for whites and nonwhites. (Note: You should have two curves in your graph, one for white people and another for non-white people – see question 4 for help with this). Keep all the dummy variables at 1 and the rest of the variables at their means. Look at your plot. Where is the difference in estimated probabilities of loan approval larger? At high levels of loanprc or at low levels of loanprc? At _______ (high/low) levels of loanprc.10 points Question 111. Estimate the multiple regression model using logit instead. Check the fit of this model, by computing the percentage of correct predictions you get from this estimation. You should also check the percentage of correct predictions among the people who got their loan approved and the percentage of correct predictions for those people who got their loan rejected. Blank 1 percent of the loan approval status of the people in this sample is correctly predicted by this logit model. However, only Blank 2 percent of rejected loans are correctly predicted by this model. (Express your answers in percentage points. Round both answers to 1 decimal point. For example, if your answer is 93.78%, enter 93.8).10 points Question 121. You estimated a logit in question 11. Look at the output of that estimation. What is the value of the maximized log likelihood function? Blank 1 (Round to 2 decimal points; don’t forget to enter the negative sign in your answer)Now, estimate a logit only on a constant. The command is pretty simple: logit approve.What is the value of the log likelihood function for this very simple logit (a logit without any explanatory variables)? Blank 2 (Round to 2 decimal points; don’t forget to enter the negative sign in your answer)Now, take the ratio of the maximized log likelihood from question 11 to the maximized log likelihood from the simple logit on a constant only. Call this ratio x. What is the value of 1-x? Blank 3 (Enter the answer in decimals. Round your answer to 3 decimals).Now look back at the output of question 11 and check that this last value is similar to the pseudo-Rsquared reported there.